1 /*- 2 * Copyright (c) 2017 Steven G. Kargl 3 * All rights reserved. 4 * 5 * Redistribution and use in source and binary forms, with or without 6 * modification, are permitted provided that the following conditions 7 * are met: 8 * 1. Redistributions of source code must retain the above copyright 9 * notice unmodified, this list of conditions, and the following 10 * disclaimer. 11 * 2. Redistributions in binary form must reproduce the above copyright 12 * notice, this list of conditions and the following disclaimer in the 13 * documentation and/or other materials provided with the distribution. 14 * 15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR 16 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES 17 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. 18 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, 19 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 20 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 21 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 22 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 23 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF 24 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 25 */ 26 27 /* 28 * See ../src/s_sinpi.c for implementation details. 29 * 30 * FIXME: This has not been compiled nor has it been tested for accuracy. 31 * FIXME: This should use bit twiddling. 32 */ 33 34 #include "math.h" 35 #include "math_private.h" 36 37 /* 38 * pi_hi contains the leading 56 bits of a 169 bit approximation for pi. 39 */ 40 static const long double 41 pi_hi = 3.14159265358979322702026593105983920e+00L, 42 pi_lo = 1.14423774522196636802434264184180742e-17L; 43 44 #include "k_cospil.h" 45 #include "k_sinpil.h" 46 47 volatile static const double vzero = 0; 48 49 long double 50 sinpil(long double x) 51 { 52 long double ax, hi, lo, s, xf, xhi, xlo; 53 uint32_t ix; 54 55 ax = fabsl(x); 56 57 if (ax < 1) { 58 if (ax < 0.25) { 59 if (ax < 0x1p-60) { 60 if (x == 0) 61 return (x); 62 hi = (double)x; 63 hi *= 0x1p113L; 64 lo = x * 0x1p113L - hi; 65 s = (pi_lo + pi_hi) * lo + pi_lo * lo + 66 pi_hi * hi; 67 return (s * 0x1p-113L); 68 } 69 70 s = __kernel_sinpil(ax); 71 return (copysignl(s, x)); 72 } 73 74 if (ax < 0.5) 75 s = __kernel_cospil(0.5 - ax); 76 else if (ax < 0.75) 77 s = __kernel_cospil(ax - 0.5); 78 else 79 s = __kernel_sinpil(1 - ax); 80 return (copysignl(s, x)); 81 } 82 83 if (ax < 0x1p112) { 84 xf = floorl(ax); 85 ax -= xf; 86 if (ax == 0) { 87 s = 0; 88 } else { 89 if (ax < 0.5) { 90 if (ax <= 0.25) 91 s = __kernel_sinpil(ax); 92 else 93 s = __kernel_cospil(0.5 - ax); 94 } else { 95 if (ax < 0.75) 96 s = __kernel_cospil(ax - 0.5); 97 else 98 s = __kernel_sinpil(1 - ax); 99 } 100 101 if (xf > 0x1p50) 102 xf -= 0x1p50; 103 if (xf > 0x1p30) 104 xf -= 0x1p30; 105 ix = (uint32_t)xf; 106 if (ix & 1) s = -s; 107 } 108 return (copysignl(s, x)); 109 } 110 111 if (isinf(x) || isnan(x)) 112 return (vzero / vzero); 113 114 /* 115 * |x| >= 0x1p112 is always an integer, so return +-0. 116 */ 117 return (copysignl(0, x)); 118 } 119